Well-known member

Two typical causes
The server is getting overloaded (if on shared hosting) and resources are limited
or
You are under a DDOS attack that is using up your system resources

In the first, your hosting provider has to address the issue
In the latter you need to check the logs and engage a firewall to intercept (hardware or software). If WordPress DDOS pingback attack (a layer 7) it will be harder to mitigate on a shared hosting provider. What happens with the ping back attack is it basically uses up all your resources and your HTTP server quits responding.